International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 8, Pages 453-458

One-sided complements and solutions of the equation aXb=c in semirings

Sam L. Blyumin1 and Jonathan S. Golan2

1Lipetsk State Technical University, Lipetsk 398055, Russia
2Department of Mathematics, University of Haifa, Haifa 31905, Israel

Received 22 July 2001

Copyright © 2002 Sam L. Blyumin and Jonathan S. Golan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Given multiplicatively-regular elements a and b in a semiring R, and given an element c of R, we find a complete set of solutions to the equation aXb=c. This result is then extended to equations over matrix semirings.